Q-space nuclear magnetic resonance (NMR) is an experimental and theoretical framework to characterize features of the displacement distribution of translating spin-labeled molecules [3, 4]. Specifically, a pulsed-gradient NMR experiment is used to measure the “average propagator” P(r) of spin-labeled molecules directly from the magnetic resonance (MR) echo using a Fourier transform relationship. In general, as used herein, the average propagator P(r) refers to a mathematical function that describes the probability of a particle having a displacement, r, during a diffusion time period, t.
The power and utility of q-space NMR and MRI stems from its ability to characterize random and bulk molecular displacements in optically turbid media without needing to invoke a specific model of the translational diffusion process or of the material's microstructure. In fact, the specific model of the translational diffusion process and the material's microstructure can often be inferred from the MR data itself. For instance, by examining the dependence of the MR signal as a function of the diffusion time, and of the length scale probed (as measured by the q vector), useful morphological features can be extracted, particularly in porous media, such as the pore size and even the size distribution of pores, tubes, and plates. [3, 4]
Three-dimensional q-space magnetic resonance imaging (3-D q-space MRI) entails combining a q-space NMR experiment with a conventional MRI [1, 4]. The three-dimensional q-space magnetic resonance imaging can be accomplished by performing a NMR q-space experiment followed by an imaging sequence (q-space filtering), or even embedding an NMR experiment within a conventional MRI sequence. Either way, a 3-D q-space NMR experiment can be performed voxel-by-voxel within an imaging volume [1, 4]. This imaging modality can provide local information about material microstructure and microdynamics in heterogeneous, anisotropic specimen or samples, which are homogeneous on the length scale of a pixel or voxel.
The potential for 3-D q-space MRI, particularly in biological and clinical applications, is enormous but has yet to be realized. In one application, differences in features of the average propagator in neurological disorders, such as multiple sclerosis (MS) have been shown [5]. In another possible application, information provided by the average propagator is used to resolve nerve or muscle fiber bundles in regions where such fibers cross. Because of the recently demonstrated strong orientational dependence of the q-space data with fiber angle, there is a suggestion that 3-D q-space imaging may significantly improve the resolution of fiber orientation beyond that provided by diffusion tensor MRI [6, 7].
However, there are a number of significant obstacles that currently preclude the application of 3-D q-space MRI in vivo. First, it is not feasible to satisfy the “short pulse gradient” approximation in animal and human MRI systems, because the rapidly switched currents required to produce such gradients induce electric fields in the body that would exceed the current U.S. Food and Drug Administration (FDA) threshold for cardiac, CNS and peripheral nerve stimulation. This short pulse condition is required for the 3-D Fourier transform relationship between the displacement distribution and the MR signal to be strictly valid. To ameliorate this problem, a longer duration, smaller amplitude magnetic field gradients may be used. While this procedure precludes measuring the displacement distribution directly, the procedure permits measuring the average propagator, which is a smoothed version of this distribution.
Second, a more significant obstacle to performing 3-D q-space MRI is the large number of diffusion weighted MRI data points required to reconstruct the average propagator. Using the classical method of 3-D q-space MRI [1,4], which was later recast as diffusion spectrum imaging (DSI) [8], the average propagator is obtained from a 3-D inverse fast Fourier transform (IFFT) of diffusion-weighted (DW) signal attenuation E(q) data that is sampled uniformly over the 3-D q-space. However, thousands of diffusion-weighted image (DWI) data samples are needed for this approach, which makes it infeasible for routine animal and clinical imaging. For instance, a recent study of ischemia in a rat brain took 36 hours to acquire sufficient q-space data to be able to reconstruct the average propagator. [20, 21]
To address this burden of long MR scans, several methods have been proposed to reconstruct particular features of the average propagator while using a reduced number of acquisitions. For example, q-ball MRI was introduced to provide an estimate of the radially averaged propagator or orientational distribution function (ODF) [9]. Other analysis methods have been proposed to try to reconstruct features of the ODF, such as persistent angular structure MRI (PAS-MRI) [10, 11] and generalized diffusion tensor MRI (GDTI) [12, 13]. All of these methods entail acquiring a high angular resolution diffusion imaging (HARDI) data set, using a smaller number (e.g., 256) of DWI acquisitions sampled on a spherical shell in q-space.
While providing useful information about the orientation bias of diffusion in tissue and possibly other anisotropic media, the ODF itself contains only a small part of the total information content provided by the average propagator. For instance, from the ODF, one cannot recover the Gaussian part of the average propagator that provides the same information provided by diffusion tensor MRI (DTI) [14], or the statistical features of the average propagator, including high-order moments.
What is needed is a technique to estimate the entire average propagator from MR data but using a vastly reduced number of DWIs than is presently required.